Question

QUESTION 9

A bottling company uses a machine to fill bottles with olive oil. The bottles are designed to contain 475 mililitters. In fact, the contents vary according to a normal distribution with a mean of 479 mililitters and standard deviation of 5 mililitters.

Nine bottles are randomly chosen and the total amount of olive oil in the nine bottles is measured, which is supposed to be 4275 mililitters if there is no error. What is the probability that the total amount of olive oil is less than 4275 mililitters?

   a.  
0.009%

   b.  
0.820%

   c.  
0.621%

   d.  
1.222%

   e.  
0.135%

Answer 1

Solution:-

µ = 479

σ = 5

n = 9

Total = 4275

x̅ = 4275 / 9 = 475

S = σ / √9 = 5 / 3 = 1.67

P(X < 4275) = P (x̅ < 475)

                        = P (Z < 475 – 479 / 1.67)

                        = P (Z < -4 / 1.67)

                        = P (Z < -2.40)

                        = 0.0082 or 0.820%

SO the correct option is (b) 0.820%